On October 9th 2022, the Swift-BAT telescope detected a spectacular transient event, soon classified as a Gamma-Ray Burst (GRB), based on the Fermi-GBM observation performed one hour earlier. Photons up to TeV energies were observed from such GRB by LHAASO, corresponding to the highest energy ever detected from a GRB. Just after this detection, a large number of observatories detected and characterized the multi-wavelength and multi-messenger emissions of this GRB, in one of the largest worldwide follow-up campaigns ever.

The KM3NeT neutrino telescope was one of the experiments that participated in the follow-up effort. KM3NeT is currently being built in the Mediterranean Sea and is composed of two detectors: ORCA, optimized for the detection of signals induced by neutrinos in the GeV-TeV range, and ARCA, mainly focused in neutrinos at the TeV-PeV range. MeV neutrinos can also be detected by looking for rate coincidences of Photo-Multipliers Tubes signals in both detectors. A first fast analysis was performed using data from the online reconstruction chain. In this contribution, we present a refined follow-up analysis, where new offline features are added together with improved calibration and optimized event selection.